Research Article
BibTex RIS Cite

Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions

Year 2019, Volume: 7 Issue: 2, 225 - 236, 15.10.2019
https://doi.org/10.36753/mathenot.634516

Abstract

In this study, firstly the definition of operator $(\alpha,m)$-convex function is defined. Secondly, a new lemma is given. Then, new theorems are obtained in terms of this lemma. Finally, they are applied for synchronous and asynchronous functions.

References

  • \bibitem{Furita} Furuta, T., Hot, L. M., $Pe\breve{c}ari\acute{c}$, J. and Seo, Y., Mond-$Pe\breve{c}ari\acute{c}$ Method in Operator Inequalites. Inequalites for Bounded Selfadjoint Operators on a Hilbert space. Element, Zagreb, 2005.
  • \bibitem{Mihesan} Mihe\c{s}an, V. G., A generalization of the convexity, Seminar on Functionel Equations, Approx Convex, Cluj-Napoca (Romania), 1993.
  • \bibitem{MN} Moslehian, M. S. and Najafi, H., Around operator monotone functions. \emph{Integr. Equ. Oper. Theory.}, 2011, 71:575-582.
  • \bibitem{Dra} Dragomir, S. S., The Hermite-Hadamard type inequalites for operator convex functions. \emph{Appl. Math. Comput.}, 2011, 218(3):766-772.
  • \bibitem{YES} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., The Hermite-Hadamard Type inequalities for operator $m$-convex functions in Hilbert Space, \emph{Journal of New Theory}, 5(2015), 80-91.
  • \bibitem{Y.E.S} Sala\c{s}, S., Unluyol, E. and Erda\c{s}, Y., The Hermite-Hadamard Type Inequalities for Operator p-Convex Functions in Hilbert Space, \emph{Journal of New Theory}, 4(2015), 74-79.
  • \bibitem{R} Rooin, J., Alikhani, A. and Moslehian, M.S., Operator $m$-convex functions. \emph{Georgian Math. J.} 25(2018), no.1, 93-107.
  • \bibitem{G3} Ghazanfari, A. G., The Hermite-Hadamard type inequalities for operator $s$-convex functions, \emph{JARPM}, Vol:6, Issue:3, 2014, 52-61.
  • \bibitem{GB} Ghazanfari, A. G. and Barani, A., Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach \emph{J. Math. Anal.} 9(2015), no.2, 9-20.
  • \bibitem{SSC} Dragomir, S. S., $\breve{C}eby\breve{s}ev's$ type inequalities for functions of selfadjoint operators in Hilbert spaces, \emph{Linear and Multilinear Algebra}, 58(2010) no. 7-8, 805-814.
  • \bibitem{YES1} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., Some new inequalities of operator $m$-convex functions and applications for Synchronous-Asynchronous functions, accepted and press 2019 in \emph{Complex Anal. Oper. Theory}.
Year 2019, Volume: 7 Issue: 2, 225 - 236, 15.10.2019
https://doi.org/10.36753/mathenot.634516

Abstract

References

  • \bibitem{Furita} Furuta, T., Hot, L. M., $Pe\breve{c}ari\acute{c}$, J. and Seo, Y., Mond-$Pe\breve{c}ari\acute{c}$ Method in Operator Inequalites. Inequalites for Bounded Selfadjoint Operators on a Hilbert space. Element, Zagreb, 2005.
  • \bibitem{Mihesan} Mihe\c{s}an, V. G., A generalization of the convexity, Seminar on Functionel Equations, Approx Convex, Cluj-Napoca (Romania), 1993.
  • \bibitem{MN} Moslehian, M. S. and Najafi, H., Around operator monotone functions. \emph{Integr. Equ. Oper. Theory.}, 2011, 71:575-582.
  • \bibitem{Dra} Dragomir, S. S., The Hermite-Hadamard type inequalites for operator convex functions. \emph{Appl. Math. Comput.}, 2011, 218(3):766-772.
  • \bibitem{YES} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., The Hermite-Hadamard Type inequalities for operator $m$-convex functions in Hilbert Space, \emph{Journal of New Theory}, 5(2015), 80-91.
  • \bibitem{Y.E.S} Sala\c{s}, S., Unluyol, E. and Erda\c{s}, Y., The Hermite-Hadamard Type Inequalities for Operator p-Convex Functions in Hilbert Space, \emph{Journal of New Theory}, 4(2015), 74-79.
  • \bibitem{R} Rooin, J., Alikhani, A. and Moslehian, M.S., Operator $m$-convex functions. \emph{Georgian Math. J.} 25(2018), no.1, 93-107.
  • \bibitem{G3} Ghazanfari, A. G., The Hermite-Hadamard type inequalities for operator $s$-convex functions, \emph{JARPM}, Vol:6, Issue:3, 2014, 52-61.
  • \bibitem{GB} Ghazanfari, A. G. and Barani, A., Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach \emph{J. Math. Anal.} 9(2015), no.2, 9-20.
  • \bibitem{SSC} Dragomir, S. S., $\breve{C}eby\breve{s}ev's$ type inequalities for functions of selfadjoint operators in Hilbert spaces, \emph{Linear and Multilinear Algebra}, 58(2010) no. 7-8, 805-814.
  • \bibitem{YES1} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., Some new inequalities of operator $m$-convex functions and applications for Synchronous-Asynchronous functions, accepted and press 2019 in \emph{Complex Anal. Oper. Theory}.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Erdal Ünlüyol

Yeter Erdaş

Seren Salaş This is me

Publication Date October 15, 2019
Submission Date January 25, 2019
Acceptance Date September 27, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Ünlüyol, E., Erdaş, Y., & Salaş, S. (2019). Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Mathematical Sciences and Applications E-Notes, 7(2), 225-236. https://doi.org/10.36753/mathenot.634516
AMA Ünlüyol E, Erdaş Y, Salaş S. Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Math. Sci. Appl. E-Notes. October 2019;7(2):225-236. doi:10.36753/mathenot.634516
Chicago Ünlüyol, Erdal, Yeter Erdaş, and Seren Salaş. “Operator $(\alpha,m)$-Convex Functions and Applications for Synchronous and Asynchronous Functions”. Mathematical Sciences and Applications E-Notes 7, no. 2 (October 2019): 225-36. https://doi.org/10.36753/mathenot.634516.
EndNote Ünlüyol E, Erdaş Y, Salaş S (October 1, 2019) Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Mathematical Sciences and Applications E-Notes 7 2 225–236.
IEEE E. Ünlüyol, Y. Erdaş, and S. Salaş, “Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions”, Math. Sci. Appl. E-Notes, vol. 7, no. 2, pp. 225–236, 2019, doi: 10.36753/mathenot.634516.
ISNAD Ünlüyol, Erdal et al. “Operator $(\alpha,m)$-Convex Functions and Applications for Synchronous and Asynchronous Functions”. Mathematical Sciences and Applications E-Notes 7/2 (October 2019), 225-236. https://doi.org/10.36753/mathenot.634516.
JAMA Ünlüyol E, Erdaş Y, Salaş S. Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Math. Sci. Appl. E-Notes. 2019;7:225–236.
MLA Ünlüyol, Erdal et al. “Operator $(\alpha,m)$-Convex Functions and Applications for Synchronous and Asynchronous Functions”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 2, 2019, pp. 225-36, doi:10.36753/mathenot.634516.
Vancouver Ünlüyol E, Erdaş Y, Salaş S. Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Math. Sci. Appl. E-Notes. 2019;7(2):225-36.

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.